Even if you don't go to her, make sure you don't speak to her or pay her attention when she cries...even from over the other side of the room. Some time should be spent with her in one room and you in another out of sight although not all the time.
If she cries louder, it's obvious that she's having a hard time being left alone at the moment but allowing her to be with you all the time would just make that even worse because there is bound to come times where it is impossible to not leave her on her own...and I can't imagine you wanting that being as she sounds pretty vocal as it is. With full on seperation anxiety, it's not just the noise, it's also the destroying of anything they can get hold of and defecating all over the place...not so much because they need the loo but out of pure stress.

The breeders may have played a part in it if they reared the pups in the house and always had somebody there with them and they were never left in a room on their own. With seperation anxiety, it is usually the presence of people that matter...not other dogs.

When we have had pups or taken one of our own pups from the litter, they've all been pretty good and may only whine a few times whilst they still hear you moving around but then quieten down for the night. My sisters Border collie pup was good like this too. He slept in the kitchen at first and then moved to the outhouse at night but that was partly his own choice....he went out there and wanted to stop so they put his bed in there and now he has a dog flap to get into the garden. Making as much racket as yours doesn't happen with most pups as people often believe.

Still, creating a routine might help. Dogs like routine. If you tire her out during the times she's allowed out of her pen, she'll more likely sleep once she's put away. Pups do need to sleep often so I can't imagine a young pup having the energy to cry non stop 24/7.
If she does ever spend time on her own without making a noise, even if it's only a few seconds, if you're there, go back in and give her plenty of praise and then up the amount of time gradually that she is required to stay silent. This helps reinforce their confidence at being left on their own. They realise you always come back and are happy and rewarding when you do.
Also, don't make too much fuss when you go to leave her. This reinforces the noisey behaviour. A cool departure and a warm return are what it's about.
With dogs that have seperation anxiety, you find it's the opposite...the owner knows the dog hates being left and that they destroy things so they make a lot of fuss, telling the dog to behave or trying to reassure it and then when they return and find another total mess, they get angry at the dog and so it's a warm departure and cool return....this just makes the whole behaviour worse.